Proyecciones
Vol. 24, No 1, pp. 65-78, May 2005.
Universidad Católica del Norte
Antofagasta - Chile

REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*

RICARDO L. SOTO
Universidad Católica del Norte, Chile.

Correspondencia a :

ABSTRACT

Let Λ= {λ1, λ2, . . . , λn} be a set of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and su.cient conditions in order that Λmay be the spectrum of an entrywise nonnegative n × n matrix. If there exists a nonnegative matrix A with spectrum Λ we say that Λ is realized by A.If the matrix A must be symmetric we have the symmetric nonnegative inverse eigenvalue problem (SNIEP). This paper presents a simple realizability criterion by symmetric nonnegative matrices. The proof is constructive in the sense that one can explicitly construct symmetric nonnegative matrices realizing Λ.

Key words: symmetric nonnegative inverse eigenvalue problem.

AMS classification: 15A18, 15A51.

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Received : March 2005, Accepted : May 2005.

*Supported by Fondecyt 1050026, Chile.

Ricardo L. Soto
Departamento de Matemáticas
Universidad Católica del Norte
Casilla 1280
Antofagasta
Chile
e-mail : rsoto@ucn.cl